[Mr Guy]

And actually, after thinking about it more, I'm not sure it's possible for that to be the case. Granted, it's late, and I've taken some cold medicine and a sleeping pill because I've been sick.

However, think of it this way. You set your focus to be a certain distance to the subject's eyes. Pivoting the camera creates an arc of focal range exactly that distance. Assuming the pivot point remains the same (ie, you don't actually MOVE the camera's sensor, at all), the eyes will ALWAYS remain on that arc while you pivot the camera, because they will always be that exact distance away. I was wrong before thinking of the two distances as a right triangle, when you will in fact always be creating an equilateral one as you traverse the arc.

If you actually could rotate the camera perfectly around the sensor, the depth of field would actually be a three dimensional perfect sphere. As long as you don't move the sensor and merely pivot it, the eyes will remain perfectly in focus. Therefore, the real answer, I believe, is that the eyes will remain perfectly in focus as long as the ERROR in your rotation of the sensor remains within the depth of field.